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Dear Jacob,
now you have confused me almost totally.
Actually, I was first responding to the subject because I had sowhat vaguely
in mind that it might help to formulate the problem in as a
shortest-path problem (define a cost function and try to minimise it. For
example,
in the song problem, pay me $1000000 each time the subsequent song doesn't
start with the letter
the previous ended with. Otherwise, pay nothing. If you have to pay nothing
after going through the whole path, you have found a correct solution and I
am still poor.
For this sort of problem, there is a way to find the "single-source shortest
path solution"
called Dijkstra's algorithm, which is nicely described here:
_http://ciips.ee.uwa.edu.au/~morris/Year2/PLDS210/dijkstra.html_
(http://ciips.ee.uwa.edu.au/~morris/Year2/PLDS210/dijkstra.html)
I feel that the way this algorithm works should tell one also how to
implement paths
as data structures (there is (non Ruby-) code and an animation on that
website).
My confusion is about your use of multiple criteria/connections/... .
In the original version of Dijsktra's algorithm, there is only one connection
from each edge to each other.
I feel that that's also enough, somehow, because you are assigning some
overall value to a specific path in the end, and it's only because of that
that
you can put order into the set of all possible paths to choose the best.
The value you assign to a specific connection may well be a result of many
factors, but in the end, you have to come up with a numeric value for it.
Otherwise, they cannot be classified - going from New York to Philadelphia
by plane may be three times as expensive as going there by car, but only
two times as nice - so what do you do?
So I'd now tend to use a vector-of-factors incidence matrix and to evaluate
these to assign a value to measure 'how nice is it to go from A to B via
i-j?'
Best regards,
Axel
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